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CBSE Class 9 Mathematics Case Study Questions

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If you’re looking for a comprehensive and reliable study resource and case study questions for class 9 CBSE, myCBSEguide is the perfect door to enter. With over 10,000 study notes, solved sample papers and practice questions, it’s got everything you need to ace your exams. Plus, it’s updated regularly to keep you aligned with the latest CBSE syllabus . So why wait? Start your journey to success with myCBSEguide today!

Significance of Mathematics in Class 9

Mathematics is an important subject for students of all ages. It helps students to develop problem-solving and critical-thinking skills, and to think logically and creatively. In addition, mathematics is essential for understanding and using many other subjects, such as science, engineering, and finance.

CBSE Class 9 is an important year for students, as it is the foundation year for the Class 10 board exams. In Class 9, students learn many important concepts in mathematics that will help them to succeed in their board exams and in their future studies. Therefore, it is essential for students to understand and master the concepts taught in Class 9 Mathematics .

Case studies in Class 9 Mathematics

A case study in mathematics is a detailed analysis of a particular mathematical problem or situation. Case studies are often used to examine the relationship between theory and practice, and to explore the connections between different areas of mathematics. Often, a case study will focus on a single problem or situation and will use a variety of methods to examine it. These methods may include algebraic, geometric, and/or statistical analysis.

Example of Case study questions in Class 9 Mathematics

The Central Board of Secondary Education (CBSE) has included case study questions in the Class 9 Mathematics paper. This means that Class 9 Mathematics students will have to solve questions based on real-life scenarios. This is a departure from the usual theoretical questions that are asked in Class 9 Mathematics exams.

The following are some examples of case study questions from Class 9 Mathematics:

Class 9 Mathematics Case study question 1

There is a square park ABCD in the middle of Saket colony in Delhi. Four children Deepak, Ashok, Arjun and Deepa went to play with their balls. The colour of the ball of Ashok, Deepak,  Arjun and Deepa are red, blue, yellow and green respectively. All four children roll their ball from centre point O in the direction of   XOY, X’OY, X’OY’ and XOY’ . Their balls stopped as shown in the above image.

Answer the following questions:

Answer Key:

Class 9 Mathematics Case study question 2

• Now he told Raju to draw another line CD as in the figure
• The teacher told Ajay to mark  ∠ AOD  as 2z
• Suraj was told to mark  ∠ AOC as 4y
• Clive Made and angle  ∠ COE = 60°
• Peter marked  ∠ BOE and  ∠ BOD as y and x respectively

Now answer the following questions:

• 2y + z = 90°
• 2y + z = 180°
• 4y + 2z = 120°
• (a) 2y + z = 90°

Class 9 Mathematics Case study question 3

• (a) 31.6 m²
• (c) 513.3 m³
• (b) 422.4 m²

Class 9 Mathematics Case study question 4

How to Answer Class 9 Mathematics Case study questions

To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.

Students need to be careful while solving the Class 9 Mathematics case study questions. They should not make any assumptions and should always check their answers. If they are stuck on a question, they should take a break and come back to it later. With some practice, the Class 9 Mathematics students will be able to crack case study questions with ease.

Class 9 Mathematics Curriculum at Glance

At the secondary level, the curriculum focuses on improving students’ ability to use Mathematics to solve real-world problems and to study the subject as a separate discipline. Students are expected to learn how to solve issues using algebraic approaches and how to apply their understanding of simple trigonometry to height and distance problems. Experimenting with numbers and geometric forms, making hypotheses, and validating them with more observations are all part of Math learning at this level.

The suggested curriculum covers number systems, algebra, geometry, trigonometry, mensuration, statistics, graphing, and coordinate geometry, among other topics. Math should be taught through activities that include the use of concrete materials, models, patterns, charts, photographs, posters, and other visual aids.

CBSE Class 9 Mathematics (Code No. 041)

Class 9 Mathematics question paper design

The CBSE Class 9 mathematics question paper design is intended to measure students’ grasp of the subject’s fundamental ideas. The paper will put their problem-solving and analytical skills to the test. Class 9 mathematics students are advised to go through the question paper pattern thoroughly before they start preparing for their examinations. This will help them understand the paper better and enable them to score maximum marks. Refer to the given Class 9 Mathematics question paper design.

QUESTION PAPER DESIGN (CLASS 9 MATHEMATICS)

myCBSEguide: Blessing in disguise

Class 9 is an important milestone in a student’s life. It is the last year of high school and the last chance to score well in the CBSE board exams. myCBSEguide is the perfect platform for students to get started on their preparations for Class 9 Mathematics. myCBSEguide provides comprehensive study material for all subjects, including practice questions, sample papers, case study questions and mock tests. It also offers tips and tricks on how to score well in exams. myCBSEguide is the perfect door to enter for class 9 CBSE preparations.

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14 thoughts on “CBSE Class 9 Mathematics Case Study Questions”

This method is not easy for me

aarti and rashika are two classmates. due to exams approaching in some days both decided to study together. during revision hour both find difficulties and they solved each other’s problems. aarti explains simplification of 2+ ?2 by rationalising the denominator and rashika explains 4+ ?2 simplification of (v10-?5)(v10+ ?5) by using the identity (a – b)(a+b). based on above information, answer the following questions: 1) what is the rationalising factor of the denominator of 2+ ?2 a) 2-?2 b) 2?2 c) 2+ ?2 by rationalising the denominator of aarti got the answer d) a) 4+3?2 b) 3+?2 c) 3-?2 4+ ?2 2+ ?2 d) 2-?3 the identity applied to solve (?10-?5) (v10+ ?5) is a) (a+b)(a – b) = (a – b)² c) (a – b)(a+b) = a² – b² d) (a-b)(a+b)=2(a² + b²) ii) b) (a+b)(a – b) = (a + b

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CBSE Case Study Questions for Class 9 Maths - Pdf PDF Download

CBSE Case Study Questions for Class  9 Maths

CBSE Case Study Questions for Class 9 Maths are a type of assessment where students are given a real-world scenario or situation and they need to apply mathematical concepts to solve the problem. These types of questions help students to develop their problem-solving skills and apply their knowledge of mathematics to real-life situations.

Chapter Wise Case Based Questions for Class 9 Maths

The CBSE Class 9 Case Based Questions can be accessed from Chapetrwise Links provided below:

Chapter-wise case-based questions for Class 9 Maths are a set of questions based on specific chapters or topics covered in the maths textbook. These questions are designed to help students apply their understanding of mathematical concepts to real-world situations and events.

Chapter 1: Number System

• Case Based Questions: Number System

Chapter 2: Polynomial

• Case Based Questions: Polynomial

Chapter 3: Coordinate Geometry

• Case Based Questions: Coordinate Geometry

Chapter 4: Linear Equations

• Case Based Questions: Linear Equations - 1
• Case Based Questions: Linear Equations -2

Chapter 5: Introduction to Euclid’s Geometry

• Case Based Questions: Lines and Angles

Chapter 7: Triangles

• Case Based Questions: Triangles

Chapter 8: Quadrilaterals

• Case Based Questions: Quadrilaterals - 1
• Case Based Questions: Quadrilaterals - 2

Chapter 9: Areas of Parallelograms

• Case Based Questions: Circles

Chapter 11: Constructions

• Case Based Questions: Constructions

Chapter 12: Heron’s Formula

• Case Based Questions: Heron’s Formula

Chapter 13: Surface Areas and Volumes

• Case Based Questions: Surface Areas and Volumes

Chapter 14: Statistics

• Case Based Questions: Statistics

Chapter 15: Probability

• Case Based Questions: Probability

Weightage of Case Based Questions in Class 9 Maths

Why are Case Study Questions important in Maths Class  9?

• Enhance critical thinking:  Case study questions require students to analyze a real-life scenario and think critically to identify the problem and come up with possible solutions. This enhances their critical thinking and problem-solving skills.
• Apply theoretical concepts:  Case study questions allow students to apply theoretical concepts that they have learned in the classroom to real-life situations. This helps them to understand the practical application of the concepts and reinforces their learning.
• Develop decision-making skills:  Case study questions challenge students to make decisions based on the information provided in the scenario. This helps them to develop their decision-making skills and learn how to make informed decisions.
• Improve communication skills:  Case study questions often require students to present their findings and recommendations in written or oral form. This helps them to improve their communication skills and learn how to present their ideas effectively.
• Enhance teamwork skills:  Case study questions can also be done in groups, which helps students to develop teamwork skills and learn how to work collaboratively to solve problems.

In summary, case study questions are important in Class 9 because they enhance critical thinking, apply theoretical concepts, develop decision-making skills, improve communication skills, and enhance teamwork skills. They provide a practical and engaging way for students to learn and apply their knowledge and skills to real-life situations.

Class 9 Maths Curriculum at Glance

The Class 9 Maths curriculum in India covers a wide range of topics and concepts. Here is a brief overview of the Maths curriculum at a glance:

• Number Systems:  Students learn about the real number system, irrational numbers, rational numbers, decimal representation of rational numbers, and their properties.
• Algebra:  The Algebra section includes topics such as polynomials, linear equations in two variables, quadratic equations, and their solutions.
• Coordinate Geometry:  Students learn about the coordinate plane, distance formula, section formula, and slope of a line.
• Geometry:  This section includes topics such as Euclid’s geometry, lines and angles, triangles, and circles.
• Trigonometry: Students learn about trigonometric ratios, trigonometric identities, and their applications.
• Mensuration: This section includes topics such as area, volume, surface area, and their applications.
• Statistics and Probability:  Students learn about measures of central tendency, graphical representation of data, and probability.

The Class 9 Maths curriculum is designed to provide a strong foundation in mathematics and prepare students for higher education in the field. The curriculum is structured to develop critical thinking, problem-solving, and analytical skills, and to promote the application of mathematical concepts in real-life situations. The curriculum is also designed to help students prepare for competitive exams and develop a strong mathematical base for future academic and professional pursuits.

Students can also access Case Based Questions of all subjects of CBSE Class 9

• Case Based Questions for Class 9 Science
• Case Based Questions for Class 9 Social Science
• Case Based Questions for Class 9 English
• Case Based Questions for Class 9 Hindi
• Case Based Questions for Class 9 Sanskrit

Frequently Asked Questions (FAQs) on Case Based Questions for Class 9 Maths

What is case-based questions.

Case-Based Questions (CBQs) are open-ended problem solving tasks that require students to draw upon their knowledge of Maths concepts and processes to solve a novel problem. CBQs are often used as formative or summative assessments, as they can provide insights into how students reason through and apply mathematical principles in real-world problems.

What are case-based questions in Maths?

Case-based questions in Maths are problem-solving tasks that require students to apply their mathematical knowledge and skills to real-world situations or scenarios.

What are some common types of case-based questions in class 9 Maths?

Common types of case-based questions in class 9 Maths include word problems, real-world scenarios, and mathematical modeling tasks.

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FAQs on CBSE Case Study Questions for Class 9 Maths - Pdf

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CBSE Class 9th Maths 2023 : 30 Most Important Case Study Questions with Answers; Download PDF

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CBSE Class 9 Maths exam 2022-23 will have a set of questions based on case studies in the form of MCQs. CBSE Class 9 Maths Question Bank on Case Studies given in this article can be very helpful in understanding the new format of questions.

Each question has five sub-questions, each followed by four options and one correct answer. Students can easily download these questions in PDF format and refer to them for exam preparation.

CBSE Class 9 All Students can also Download here Class 9 Other Study Materials in PDF Format.

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Heron’s Formula Class 9 Extra Questions Maths Chapter 12 with Solutions Answers

May 28, 2022 by Prasanna

Here we are providing Heron’s Formula Class 9 Extra Questions Maths Chapter 12 with Answers Solutions, Extra Questions for Class 9 Maths  was designed by subject expert teachers.

Extra Questions for Class 9 Maths Heron’s Formula with Answers Solutions

Extra Questions for Class 9 Maths Chapter 12 Heron’s Formula with Solutions Answers

Heron’s Formula Class 9 Extra Questions Very Short Answer Type

Question 1. Find the area of an equilateral triangle having side 6 cm. Solutioin: Area of an equilateral triangle = \(\frac{\sqrt{3}}{4}\) × (side) 2 = \(\frac{\sqrt{3}}{4}\) × 6 × 6 = 9√3 cm 2

Heron’s Formula Class 9 Extra Questions Short Answer Type 2

CBSE Class 10 Maths Formulas for Chapter 4 Quadratic Equations are mentioned in this article.

Heron’s Formula Class 9 Extra Questions Long Answer Type

Heron’s Formula Class 9 Extra Questions HOTS

Now, area of orange shaded paper in kite = Area of ∆AOD + Area of ∆CEF = 450 cm 2 + 198.4 cm 2 = 648.4 cm 2 Area of blue shaded paper in kite = Area of ∆AOB + Area of ∆COD = 450 cm 2 + 450 cm 2 = 900 cm 2 Area of black shaded paper in kite = Area of ∆BOC = 450 cm 2 .

Heron’s Formula Class 9 Extra Questions Value Based (VBQs)

NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula

NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula are provided here. Our NCERT Maths solutions contain all the questions of the NCERT textbook that are solved and explained beautifully. Here you will get complete NCERT Solutions for Class 9 Maths Chapter 12 all exercises Exercise in one place. These solutions are prepared by the subject experts and as per the latest NCERT syllabus and guidelines. CBSE Class 9 Students who wish to score good marks in the maths exam must practice these questions regularly.

Class 9 Maths Chapter 12 Heron’s Formula NCERT Solutions

Below we have provided the solutions of each exercise of the chapter. Go through the links to access the solutions of exercises you want. You should also check out our NCERT Class 9 Solutions for other subjects to score good marks in the exams.

NCERT Solutions for Class 9 Maths Chapter 12 Exercise 12.1

NCERT Solutions for Class 9 Maths Chapter 12 Exercise 12.2

NCERT Solutions for Class 9 Maths Chapter 12 – Topic Discussion

Below we have listed the topics that have been discussed in this chapter.

• Heron’s Formula

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CBSE Class 9 Maths Most Important Case Study Based Questions With Solution

Cbse class 9 mathematics case study questions.

In this post I have provided CBSE Class 9 Maths Case Study Based Questions With Solution. These questions are very important for those students who are preparing for their final class 9 maths exam.

All these questions provided in this article are with solution which will help students for solving the problems. Dear students need to practice all these questions carefully with the help of given solutions.

As you know CBSE Class 9 Maths exam will have a set of cased study based questions in the form of MCQs. CBSE Class 9 Maths Question Bank given in this article can be very helpful in understanding the new format of questions for new session.

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Case studies in class 9 mathematics.

The Central Board of Secondary Education (CBSE) has included case study based questions in the Class 9 Mathematics paper in current session. According to new pattern CBSE Class 9 Mathematics students will have to solve case based questions. This is a departure from the usual theoretical conceptual questions that are asked in Class 9 Maths exam in this year.

Each question provided in this post has five sub-questions, each followed by four options and one correct answer. All CBSE Class 9th Maths Students can easily download these questions in PDF form with the help of given download Links and refer for exam preparation.

There is many more free study materials are available at Maths And Physics With Pandey Sir website. For many more books and free study material all of you can visit at this website.

Given Below Are CBSE Class 9th Maths Case Based Questions With Their Respective Download Links.

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Case Study Questions for Class 9 Maths Chapter 12 Herons Formula

Case study questions for class 9 maths chapter 9 areas of parallelograms and triangles, case study questions for class 9 maths chapter 6 lines and angles, case study questions for class 9 maths chapter 7 triangles, case study questions for class 9 maths chapter 5 introduction to euclid’s geometry, case study and passage based questions for class 9 maths chapter 14 statistics, case study questions for class 9 maths chapter 1 real numbers, case study questions for class 9 maths chapter 4 linear equations in two variables, case study questions for class 9 maths chapter 3 coordinate geometry, case study questions for class 9 maths chapter 15 probability, case study questions for class 9 maths chapter 13 surface area and volume, case study questions for class 9 maths chapter 10 circles, case study questions for class 9 maths chapter 9 quadrilaterals, case study questions for class 9 maths chapter 2 polynomials.

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NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2

N cert solutions for class 9 maths chapter 12 heron’s formula ex 12.2.

The topics and sub-topics in NCERT Class 9 Maths Text Book Chapter 12 Heron’s Formula:

• Heron’s Formula
• Introduction
• Area Of A Triangle – By Heron’s Formula
• Application Of Heron’s Formula In Finding Areas Of Quadrilaterals

Formulae Handbook for Class 9 Maths and Science Educational Loans in India

• Herons Formula Exercise 12.1

Ex 12.2 Class 9 Maths Question 1

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• NCERT Solutions Class 9 Maths
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Ex 12.2 Class 9 Maths Question 3

Ex 12.2 Class 9 Maths Question 9

NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula (हीरोन सूत्र) (Hindi Medium) Ex 12.2

NCERT Solutions for Class 9 Maths

• Chapter 1 Number systems
• Chapter 2 Polynomials
• Chapter 3 Coordinate Geometry
• Chapter 4 Linear Equations in Two Variables
• Chapter 5 Introduction to Euclid Geometry
• Chapter 6 Lines and Angles
• Chapter 7 Triangles
• Chapter 8 Quadrilaterals
• Chapter 9 Areas of Parallelograms and Triangles
• Chapter 10 Circles
• Chapter 11 Constructions
• Chapter 12 Heron’s Formula
• Chapter 13 Surface Areas and Volumes
• Chapter 14 Statistics
• Chapter 15 Probability
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NCERT Solutions for Class 9 Maths Chapter 10 Heron's Formula

• NCERT Solutions
• Chapter 12 Herons Formula

NCERT Solutions for Maths Chapter 10 Class 9 Heron’s Formula - FREE PDF Download

NCERT Solutions for heron's formula class 9 maths ch 10 Heron’s Formula curated by our subject experts to facilitate a practical and smooth understanding of the concepts related to Heron's Formula. These NCERT Solutions can be accessed anytime and anywhere, at your convenience, to understand the concepts in a better way.  These solutions to each exercise question in the PDF are explained using a clear step-by-step method. It acts as an essential tool for you to prepare the chapter quickly and efficiently during exams. You can download and practice these NCERT Solutions for herons formula Class 9 Maths Chapter 10 to thoroughly understand the concepts covered in the chapter.

Glance on Maths Chapter 10 Class 9 - Heron's Formula

This article deals with Heron's Formula, which is a method to calculate the area of a triangle when the lengths of all three sides are known.

The questions cover topics such as finding the area of a triangle when the sides are given, finding the missing side when the area and two sides are given, and finding the height of a triangle when the area and the base are given.

Chapter 10 Maths Class 9 recalls how to calculate the perimeter of various figures and shapes.

This article contains chapter notes, exercises, explanation videos, links, and important questions for Chapter 10 - Heron's Formula where you can download a FREE PDF.

There is one exercise (6 fully solved questions) in class 9th maths chapter 10 Heron's Formula.

Access Exercise Wise NCERT Solutions for Chapter 10 Maths Class 9

Exercises Under NCERT Solutions for Class 9 Maths Chapter 10 Heron's Formula

Exercise 10.1: This exercise consists of six questions that are based on the concept of Heron's Formula. The questions cover topics such as finding the area of a triangle when the sides are given, finding the missing side when the area and two sides are given, and finding the height of a triangle when the area and the base are given. The exercise also includes word problems that require the application of Heron's Formula to find the area of triangles.

Access NCERT Solutions Maths Chapter 10 - Heron’s formula

Exercise 10.1 .

1. A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side $'a'$. Find the area of the signal board, using Heron’s formula. If its perimeter is $180\ \text{cm}$, what will be the area of the signal board?

Length of the side of traffic signal board $=a$ 

Perimeter of traffic signal board which is an equilateral triangle $=3\times a$

We know that,

$2s=$ Perimeter of the triangle, 

So, $2s=3a$

$\Rightarrow s=\dfrac{3}{2}a$

 Area of triangle can be evaluated by Heron’s formula:

$A=\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)}$

$a$ , $b$ and $c$ are the sides of the triangle

\[s=\dfrac{a+b+c}{2}\]

Substituting $s=\dfrac{3}{2}a$ in Heron’s formula, we get:

Area of given triangle:

 $A=\sqrt{\dfrac{3}{2}a\left( \dfrac{3}{2}a-a \right)\left( \dfrac{3}{2}a-a \right)\left( \dfrac{3}{2}a-a \right)}$ 

$A=\dfrac{\sqrt{3}}{2}{{a}^{2}}\ \ ......\text{(1)}$

Perimeter of traffic signal board:

$P=180\ \text{cm}$

Hence, side of traffic signal board

$a=\left( \dfrac{180}{3} \right)$

$a=60\ \ ......\text{(2)}$

Substituting Equation (2) in Equation (1), we get:

Area of traffic signal board is $A=\dfrac{\sqrt{3}}{2}{{\left( 60\,cm \right)}^{2}}$

$\Rightarrow A=\left( \dfrac{3600}{4}\sqrt{3} \right)\,c{{m}^{2}}$

$\Rightarrow A=900\sqrt{3}\,c{{m}^{2}}$

Hence, the area of the signal board is $900\sqrt{3}\text{ c}{{\text{m}}^{2}}$.

2. The triangular side walls of a flyover have been used for advertisements. The sides of the walls are $122m,\,22m,$ and $120m$. The advertisements yield on earning of Rs. $5000\,per\,{{m}^{2}}$ per year. A company hired one of its walls for $3$ months. How much rent did it pay?

Ans: The length of the sides of the triangle are (say $a$, $b$ and $c$)

$a=122\ \text{m}$

$b=22\ \text{m}$

$c=120\ \text{m}$

Perimeter of triangle = sum of the length of all sides

Perimeter of triangle is:

$P=122+22+120$

$P=264\ \text{m}$

$2s=264\ \text{m}$

$s=132\ \text{m}$

Area of triangle can be evaluated by Heron’s formula:

$a$, $b$ and $c$ are the sides of the triangle

So, in this question,

$s=\dfrac{122+22+140}{2}$

Substituting values of $s$ $a$, $b$, $c$ in Heron’s formula, we get:

Area of given triangle $=\left[ \sqrt{132\left( 132-122 \right)\left( 132-22 \right)\left( 132-120 \right)} \right]{{m}^{2}}$

$=\left[ \sqrt{132\left( 10 \right)\left( 110 \right)\left( 12 \right)} \right]\,{{m}^{2}}=1320\,{{m}^{2}}$ 

It is given that:

Rent of $1{{m}^{2}}$ area per year is:

$R=Rs.\text{ 5000/}{{\text{m}}^{2}}$ 

Rent of $1{{m}^{2}}$ area per month will be:

$R=Rs.\ \dfrac{5000}{12}/{{m}^{2}}$

Rent of $1320{{m}^{2}}$ area for $3$ months:

$R=\left( \dfrac{5000}{12}\times 3\times 1320 \right)/{{m}^{2}}$

$\Rightarrow R=Rs.\ 1650000$

Therefore, the total cost rent that company must pay is Rs. $1650000$.

3. There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN”. If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

Ans: It is given that the sides of the wall are 15 m, 11 m and 6 m.

So, the semi perimeter of triangular wall (s) = (15+11+6)/2 m = 16 m

Using Heron’s formula,

$A=\sqrt{16(16 - 15)(16 - 11)(16 - 6)}$

$A=\sqrt800 m^2$

$A=20\sqrt2 m^2$

4. Find the area of a triangle two sides of which are $18\mathbf{cm}$ and $10\mathbf{cm}$ and the perimeter is $42cm$.

Ans: Let the length of the third side of the triangle be $x$. 

Perimeter of the given triangle:

Let the sides of the triangle be $a$, $b$ and $c$.

Perimeter of the triangle = sum of all sides

$18+10+x=42$

$\Rightarrow 28+x=42$

$\Rightarrow x=14$

$\Rightarrow s=\dfrac{18+10+14}{2}$

$\Rightarrow s=21cm$

Substituting values of  $s$ $a$, $b$, $c$ in Heron’s formula, we get:

$A=\left[ \sqrt{21\left( 21-18 \right)\left( 21-10 \right)\left( 21-14 \right)} \right]$

$\Rightarrow A=\left[ \sqrt{21\left( 3 \right)\left( 11 \right)\left( 7 \right)} \right]$

$\Rightarrow A=21\sqrt{11}\text{ }c{{m}^{2}}$

Hence, the area of the given triangle is $21\sqrt{11}\text{ }c{{m}^{2}}$.

5. Sides of a triangle are in the ratio of $12:17:25$ and its perimeter is $540cm$. Find its area.

Ans: Let the common ratio between the sides of the given triangle be $x$. 

Therefore, the side of the triangle will be $12x$, $17x$, and $25x$.

It is given that,

Perimeter of this triangle $=540cm$

Perimeter = sum of the length of all sides

$12x+17x+25x=540$

$\Rightarrow 54x=540$

$\Rightarrow x=10$

Sides of the triangle will be:

\[12\times 10=120cm\]

$17\times 10=170cm$

$25\times 10=250cm$

$\Rightarrow s=\dfrac{120+170+250}{2}$

$\Rightarrow s=270cm$

$A=\left[ \sqrt{270\left( 270-120 \right)\left( 270-170 \right)\left( 270-250 \right)} \right]$

$\Rightarrow A=\left[ \sqrt{270\left( 150 \right)\left( 100 \right)\left( 20 \right)} \right]$

$\Rightarrow A=9000c{{m}^{2}}$

Therefore, the area of this triangle is $9000\,c{{m}^{2}}.$

6. An isosceles triangle has perimeter $30cm$ and each of the equal sides is $12cm$. Find the area of the triangle.

Ans: Let the third side of this triangle be $x$.

Measure of equal sides is $12cm$ as the given triangle is an isosceles triangle.

Perimeter of triangle, $P=30cm$

Perimeter of triangle = Sum of the sides 

$12+12+x=30$

$\Rightarrow x=6cm$

$\Rightarrow s=\dfrac{12+12+6}{2}$

$\Rightarrow s=15cm$

Substituting values of $s$ $a$, $b$, $c$ in Heron’s formula we get:$A=\left[ \sqrt{15\left( 15-12 \right)\left( 15-12 \right)\left( 15-6 \right)} \right]$

$\Rightarrow A=\left[ \sqrt{15\left( 3 \right)\left( 3 \right)\left( 9 \right)} \right]$

$\Rightarrow A=9\sqrt{15}c{{m}^{2}}$

Hence, the area of the given isosceles triangle is $9\sqrt{15}c{{m}^{2}}$.

Overview of Deleted Syllabus for CBSE Class 9 Maths Heron's Formula

Class 9 Maths Chapter 10: Exercises Breakdown

NCERT Solutions for Class 9 Maths Chapter 10 - Heron's Formula provides a necessary resource for students diving into the world of geometry and trigonometry. In this chapter, students are equipped with Heron's Formula, a powerful method for easily calculating triangle areas. Mastering this chapter not only enhances their understanding of geometry but also improves their problem-solving abilities. Heron's Formula is a valuable addition to their mathematical toolkit, setting a solid foundation for future studies in mathematics and various real-life scenarios where the calculation of triangle areas is essential.

Other Study Material for CBSE Class 9 Maths Chapter 10

Chapter-Specific NCERT Solutions for Class 9 Maths

Given below are the chapter-wise NCERT Solutions for Class 9 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

FAQs on NCERT Solutions for Class 9 Maths Chapter 10 Heron's Formula

1. How to find altitude in Heron's Formula class 9?

In class 9 maths herons formula , Heron's formula itself doesn't directly calculate the altitude of a triangle. However, it can be used along with the concept of area to find the altitude in a scalene triangle (one with all sides unequal). Here's the process:

Heron's formula gives the area (A) of a triangle with sides a, b, and c as:

A = $\sqrt{s(s-a)(s-b)(s-c)}$

where s is the semi-perimeter (s = (a + b + c) / 2)

The area of a triangle can also be calculated as 1/2 * base * height (where base is the side along which the altitude is drawn, and the height is the altitude itself).

By equating these two expressions for area and solving for the height (h) with base (b) known, you can get the formula for altitude using Heron's formula:

h = 2 * $\sqrt{s(s-a)(s-b)(s-c)}$ / b

2. Is Heron's formula applicable for all triangles in chapter 10 class 9 maths solutions pdf?

Yes, In class 9 ch 10 , Heron's formula is applicable to all triangles, irrespective of their type (scalene, isosceles, or equilateral). As long as you know the lengths of all three sides, you can use the formula to find the area of the triangle.

3. What is the real-life application of Heron's formula?

Suppose you have to calculate the area of a triangular land. What is the probability that the area is of a regular shape? It is impossible that you will come across lands with regular spaces and sizes, and this is where Heron’s formula comes into use. To calculate the area of real-life objects, the best way to find the exact area of the land is to use Heron’s formula.

4. What is Heron's formula?

Triangle is a three-dimensional closed shape. Heron’s formula calculates the area of a triangle when the length of all three sides is given. Using Heron's formula, we can calculate the area of any triangle, be it a scalene, isosceles or equilateral triangle. For example, the sides of a triangle are given as a, b, and c. Using Heron’s formula, the area of the triangle can be calculated by Area = √S (S-a)(S-b)(S-c) where s is the semi-perimeter of the triangle.

5. How do you solve Heron's formula questions?

To solve questions based on Heron’s formula, you need to remember Heron’s formula, Area= Area= √S (S-a)(S-b)(S-c). Here, ‘s’ is the semi-perimeter of the triangle, and a, b, and c are the lengths of the sides of the triangle. The semi perimeter is denoted by S. It can be calculated by using the formula: S = a+b+c/2. By substituting the values given in these formulas, you can calculate the area of a triangle.

6. What is the meaning of s in Heron's formula?

In Heron’s formula, Area = √S (S-a)(S-b)(S-c), where ‘s’ stands for the semi-perimeter of the triangle whose area we need to calculate. Semi-perimeter can be calculated by the given formula: S = a+b+c/2. To learn more about the semi-perimeter and its usage in calculating the area of a triangle, you can download the Vedantu app or check out the official website of  Vedantu .

7. What is a Semi-Perimeter?

In Geometry, the Semi-perimeter of any polygon is half of its perimeter. In Class 9, Chapter 12, Heron’s Formula explains the semi-perimeter of a triangle. Semi-perimeter is denoted by ‘s’ in Heron’s formula, which is Area= √s  (s-a)(s-b)(s-c) ‘s’ stands for semi-perimeter, which can be calculated by the given formula: s = a+b+c/2, where a, b, and c are the sides of the triangle of which the area has to be calculated.

8. What is a Semi-Perimeter?

In Geometry, the Semi-perimeter of any polygon is half of its perimeter. In Class 9, Chapter 12, Heron’s Formula explains the semi-perimeter of a triangle. Semi-perimeter is denoted by ‘s’ in Heron’s formula, which is Area= √s  (s-a)(s-b)(s-c)

‘s’ stands for semi-perimeter, which can be calculated by the given formula:

s = a+b+c/2, where a, b and c are the sides of the triangle of which the area has to be calculated.

NCERT Solutions for Class 9 Maths

Ncert solutions for class 9.

Class 9 Maths Case Study Questions of Chapter 1 Real Numbers

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Case study Questions in Class 9 Mathematics Chapter 1  are very important to solve for your exam. Class 9 Maths Chapter 1 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving  Class 9 Maths Case Study Questions  Chapter 1 Real Numbers

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

In CBSE Class 9 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Real Numbers Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 9 Maths Chapter 1 Real Numbers

Case Study/Passage-Based Questions

Case Study 1: A Mathematics Exhibition is being conducted in your school and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.

Observe the following factor tree and answer the following:

1. What will be the value of x?

Answer: b) 13915

2. What will be the value of y?

Answer: c) 11

3. What will be the value of z?

Answer: b) 23

4. According to the Fundamental Theorem of Arithmetic 13915 is a

a) Composite number

b) Prime number

c) Neither prime nor composite

d) Even number

Answer: a) Composite number

5. The prime factorization of 13915 is

a) 5 × 11 3  × 13 2

b) 5 × 11 3  × 23 2

c) 5 × 11 2  × 23

d) 5 × 11 2  × 13 2

Answer: c) 5 × 112 × 23

Case Study 2: Srikanth has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment questions at the end of his project as listed below. Answer them.

(i) For what value of n, 4 n  ends in 0?

(a) 10 (b) when n is even (c) when n is odd (d) no value of n

Answer: (d) no value of n3

(ii) If a is a positive rational number and n is a positive integer greater than 1, then for what value of n, an is a rational number?

(a) when n is any even integer (b) when n is any odd integer (c) for all n > 1 (d) only when n=0

Answer: (c) for all n > 1

(iii) If x and y are two odd positive integers, then which of the following is true?

(a) x 2 +y 2  is even (b) x 2 +y 2  is not divisible by 4 (c) x 2 +y 2   is odd (d) both (a) and (b)

Answer: (d) both (a) and (b)

(iv) The statement ‘One of every three consecutive positive integers is divisible by 3’ is

(a) always true (b) always false (c) sometimes true (d) None of these

Answer:(a) always true

(v) If n is any odd integer, then n 2 – 1 is divisible by

(a) 22 (b) 55 (c) 88 (d) 8

Answer: (d) 8

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 1 Real Numbers with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Real Numbers Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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• NCERT Solutions
• NCERT Class 9
• NCERT 9 Maths
• Chapter 12: Herons Formula
• Exercise 12.1

NCERT Solutions for Class 9 Maths Chapter 12 - Heron's Formula Exercise 12.1

* According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 10.

NCERT Solutions for Class 9 Maths Chapter 12 – Heron’s Formula Exercise 12.1 helps you understand Heron’s Formula with ease. From an academic perspective, this fundamental concept finds significance in a myriad of areas. Therefore, it is necessary to have a clear grasp of the concept. These solutions are designed by highly knowledgeable teachers with countless years of experience. In other words, NCERT Solutions is one of the best guides for your study needs. Relevant topics are presented in an easy-to-understand format. Moreover, we have barred the use of complex jargon. Furthermore, its content is updated regularly as per the prescribed CBSE syllabus.

Download PDF of NCERT Solutions for Class 9 Maths Chapter 12 – Heron’s Formula Exercise 12.1

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Exercise 12.2 Solutions – 9 Questions

Access Answers of Maths NCERT Class 9 Chapter 12 – Heron’s Formula Exercise 12.1

1. A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?

Side of the signal board = a

Perimeter of the signal board = 3a = 180 cm

∴ a = 60 cm

Semi perimeter of the signal board (s) = 3a/2

By using Heron’s formula,

Area of the triangular signal board will be =

2. The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m and 120 m (see Fig. 12.9). The advertisements yield an earning of ₹5000 per m 2 per year. A company hired one of its walls for 3 months. How much rent did it pay?

The sides of the triangle ABC are 122 m, 22 m and 120 m respectively.

Now, the perimeter will be (122+22+120) = 264 m

Also, the semi perimeter (s) = 264/2 = 132 m

Using Heron’s formula,

Area of the triangle =

We know that the rent of advertising per year = ₹ 5000 per m 2

∴ The rent of one wall for 3 months = Rs. (1320×5000×3)/12 = Rs. 1650000

3. There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see Fig. 12.10 ). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

It is given that the sides of the wall as 15 m, 11 m and 6 m.

So, the semi perimeter of triangular wall (s) = (15+11+6)/2 m = 16 m

Area of the message =

= √[16(16-15)(16-11) (16-6)] m 2

= √[16×1×5×10] m 2 = √800 m 2

4. Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42cm.

Assume the third side of the triangle to be “x”.

Now, the three sides of the triangle are 18 cm, 10 cm, and “x” cm

It is given that the perimeter of the triangle = 42cm

So, x = 42-(18+10) cm = 14 cm

∴ The semi perimeter of triangle = 42/2 = 21 cm

Area of the triangle,

= √[21(21-18)(21-10)(21-14)] cm 2

= √[21×3×11×7] m 2

= 21√11 cm 2

5. Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540cm. Find its area.

The ratio of the sides of the triangle are given as 12 : 17 : 25

Now, let the common ratio between the sides of the triangle be “x”

∴ The sides are 12x, 17x and 25x

It is also given that the perimeter of the triangle = 540 cm

12x+17x+25x = 540 cm

54x = 540cm

Now, the sides of triangle are 120 cm, 170 cm, 250 cm.

So, the semi perimeter of the triangle (s) = 540/2 = 270 cm

Area of the triangle

= 9000 cm 2

6. An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

First, let the third side be x.

It is given that the length of the equal sides is 12 cm and its perimeter is 30 cm.

So, 30 = 12+12+x

∴ The length of the third side = 6 cm

Thus, the semi perimeter of the isosceles triangle (s) = 30/2 cm = 15 cm

= √[15(15-12)(15-12)(15-6)] cm 2

= √[15×3×3×9] cm 2

= 9√15 cm 2

Heron’s formula is used to find the area of a triangle, provided the length of the 3 sides is given. Apart from the formula, Heron contributed in many other ways, and the most notable was the invention of the very first steam engine. It was called the Aeolipile, and technically, it didn’t resemble an engine. However, no practical applications could be identified, and instead, it was used as a toy and a novelty for the ancient Greeks. Explore more about Heron’s Formula, learn how to solve related problems and more only on NCERT Solutions For Class 9 Maths .

Key Features of NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Exercise 12.1

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CBSE Case Study Questions Class 9 Maths Chapter 2 Polynomials PDF Download

CBSE Case Study Questions Class 9 Maths Chapter 2 Polynomials PDF Download  are very important to solve for your exam. Class 9 Maths Chapter 2 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Case Study Questions Class 9 Maths Chapter 2 Polynomials

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• Checkout: Class 9 Maths Case Study Questions

Polynomials Case Study Questions With Answers

Case study questions class 9 maths chapter 2.

Case Study/Passage-Based Questions

Case Study 1. Ankur and Ranjan start a new business together. The amount invested by both partners together is given by the polynomial p(x) = 4x 2 + 12x + 5, which is the product of their individual shares.

Coefficient of x 2 in the given polynomial is (a) 2 (b) 3 (c) 4 (d) 12

Answer: (c) 4

Total amount invested by both, if x = 1000 is (a) 301506 (b)370561 (c) 4012005 (d)490621

Answer: (c) 4012005

The shares of Ankur and Ranjan invested individually are (a) (2x + 1),(2x + 5)(b) (2x + 3),(x + 1) (c) (x + 1),(x + 3) (d) None of these

Answer: (a) (2x + 1),(2x + 5)

Name the polynomial of amounts invested by each partner. (a) Cubic (b) Quadratic (c) Linear (d) None of these

Answer: (c) Linear

Find the value of x, if the total amount invested is equal to 0. (a) –1/2 (b) –5/2 (c) Both (a) and (b) (d) None of these

Answer: (c) Both (a) and (b)

Case Study 2. One day, the principal of a particular school visited the classroom. The class teacher was teaching the concept of a polynomial to students. He was very much impressed by her way of teaching. To check, whether the students also understand the concept taught by her or not, he asked various questions to students. Some of them are given below. Answer them

Which one of the following is not a polynomial? (a) 4x 2 + 2x – 1 (b) y+3/y (c) x 3 – 1 (d) y 2 + 5y + 1

Answer: (b) y+3/y

The polynomial of the type ax 2 + bx + c, a = 0 is called (a) Linear polynomial (b) Quadratic polynomial (c) Cubic polynomial (d) Biquadratic polynomial

Answer: (a) Linear polynomial

The value of k, if (x – 1) is a factor of 4x 3 + 3x 2 – 4x + k, is (a) 1 (b) –2 (c) –3 (d) 3

Answer: (c) –3

If x + 2 is the factor of x 3 – 2ax 2 + 16, then value of a is (a) –7 (b) 1 (c) –1 (d) 7

Answer: (b) 1

The number of zeroes of the polynomial x 2 + 4x + 2 is (a) 1 (b) 2 (c) 3 (d) 4

Answer: (b) 2

Case Study 3. Amit and Rahul are friends who love collecting stamps. They decide to start a stamp collection club and contribute funds to purchase new stamps. They both invest a certain amount of money in the club. Let’s represent Amit’s investment by the polynomial A(x) = 3x^2 + 2x + 1 and Rahul’s investment by the polynomial R(x) = 2x^2 – 5x + 3. The sum of their investments is represented by the polynomial S(x), which is the sum of A(x) and R(x).

Q1. What is the coefficient of x^2 in Amit’s investment polynomial A(x)? (a) 3 (b) 2 (c) 1 (d) 0

Answer: (a) 3

Q2. What is the constant term in Rahul’s investment polynomial R(x)? (a) 2 (b) -5 (c) 3 (d) 0

Answer: (c) 6

Q3. What is the degree of the polynomial S(x), representing the sum of their investments? (a) 4 (b) 3 (c) 2 (d) 1

Answer: (c) 2

Q4. What is the coefficient of x in the polynomial S(x)? (a) 7 (b) -3 (c) 0 (d) 5

Answer: (b) -3

Q5. What is the sum of their investments, represented by the polynomial S(x)? (a) 5x^2 + 7x + 4 (b) 5x^2 – 3x + 4 (c) 5x^2 – 3x + 5 (d) 5x^2 + 7x + 5

Answer: (b) 5x^2 – 3x + 4

Case Study 4. A school is organizing a fundraising event to support a local charity. The students are divided into three groups: Group A, Group B, and Group C. Each group is responsible for collecting donations from different areas of the town.

Group A consists of 30 students and each student is expected to collect ‘x’ amount of money. The polynomial representing the total amount collected by Group A is given as A(x) = 2x^2 + 5x + 10.

Group B consists of 20 students and each student is expected to collect ‘y’ amount of money. The polynomial representing the total amount collected by Group B is given as B(y) = 3y^2 – 4y + 7.

Group C consists of 40 students and each student is expected to collect ‘z’ amount of money. The polynomial representing the total amount collected by Group C is given as C(z) = 4z^2 + 3z – 2.

Q1. What is the coefficient of x in the polynomial A(x)? (a) 2 (b) 5 (c) 10 (d) 0

Answer: (b) 5

Q2. What is the degree of the polynomial B(y)? (a) 2 (b) 3 (c) 4 (d) 1

Answer: (b) 3

Q3. What is the constant term in the polynomial C(z)? (a) 4 (b) 3 (c) -2 (d) 0

Answer: (c) -2

Q4. What is the sum of the coefficients of the polynomial A(x)? (a) 2 (b) 5 (c) 10 (d) 17

Answer: (c) 10

Q5. What is the total number of students in all three groups combined? (a) 30 (b) 20 (c) 40 (d) 90

Answer: (c) 40

Hope the information shed above regarding Case Study and Passage Based Questions for Case Study Questions Class 9 Maths Chapter 2 Polynomials with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Polynomials Case Study and Passage-Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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